(1+ε)-Optimal MDS Codes: Contacting Any Set of Helper Nodes Smaller Than n-1

(1+ε)-optimal Maximum Distance Separable ((1+ε)-optimal MDS) codes, which are a special kind of $(n, k)$ MDS codes, can repair a single failed node by downloading slightly sub-optimal amount of data from $d$ helper nodes where $d\in [k, n)$, and have small sub-packetization level. Some (1+ε)-optimal MDS codes have been constructed in the literatures. However, for all the existing (1+ε)-optimal MDS codes with the number of helper nodes $d$ smaller than $n-1$, a few compulsory nodes need to be contacted when repairing a failed node. In this paper, we provide two explicit (1+ε)-optimal MDS codes contacting any set of $d$ helper nodes with $d$ smaller than $n-1$ for the first time.